For those of you who insist on being very careful with your
language, energy is NOT quantized, action is quantized. It is quite
possible to have an atom in a superposition of two distinct energy
eigenstates. The situation that I am most knowledgable about, atoms are
created in a superposition of two excited states that decay at different
rates. It is possible to observe oscillations between the states which
is called quatum beats.
Over long periods of time, energy becomes quantized and thus for
stable energy levels one has stability.